Bell's theorem as a signature of nonlocality: a classical counterexample

TL;DR

This paper presents a classical model with local interactions that can violate Bell inequalities, challenging the idea that such violations are exclusive signatures of quantum nonlocality.

Contribution

It introduces a classical probabilistic model that reproduces Bell inequality violations, questioning their role as indicators of nonlocality.

Findings

Classical phase-space distributions analogous to quantum states.

Bell inequalities are violated under certain detector interactions.

Violations occur even with local, conserved angular momentum models.

Abstract

For a system composed of two particles Bell's theorem asserts that averages of physical quantities determined from local variables must conform to a family of inequalities. In this work we show that a classical model containing a local probabilistic interaction in the measurement process can lead to a violation of the Bell inequalities. We first introduce two-particle phase-space distributions in classical mechanics constructed to be the analogs of quantum mechanical angular momentum eigenstates. These distributions are then employed in four schemes characterized by different types of detectors measuring the angular momenta. When the model includes an interaction between the detector and the measured particle leading to ensemble dependencies, the relevant Bell inequalities are violated if total angular momentum is required to be conserved. The violation is explained by identifying assumptions made in the derivation of Bell's theorem that are not fulfilled by the model. These assumptions will be argued to be too restrictive to see in the violation of the Bell inequalities a faithful signature of nonlocality.